Question: Marcus is picking songs to play during a slideshow. The songs are each $3\dfrac12$ minutes long. The slideshow is $31\dfrac12$ minutes long. How many songs will play in the slideshow?
We can think about this problem like this: $ {\text{number of songs}} = {\text{total time}} \div {\text{length of each song}}$ ${\text{?}} = {31\dfrac12 \text{min}} \div {3\dfrac{1}{2} \text{min}}$ $\phantom{?} = {\dfrac{63}{2} \text{min}} \div {\dfrac{7}{2} \text{min}} ~~~~~~~{\text{Rewrite } {31\dfrac12} \text{ as } { \dfrac{63}{2}} \text{ and }{3\dfrac{1}{2}} \text{ as } {\dfrac{7}{2}}}$ $\phantom{?} = {\dfrac{63}{2}} \times \dfrac{2}{7} ~~~~~~~{\text{Rewrite dividing by} {\dfrac{7}{2}} \text{ as multiplying by} \dfrac{2}{7}}$ $\phantom{?} =\dfrac{63 \times 2}{2 \times 7}$ $\phantom{?} =\dfrac{126}{14}$ $\phantom{?} = {9 \text{ songs}}$ There will be $9$ songs in the slideshow.